Determination method of Markstein number based on wavenumber measurement of cellular flames at the onset of parametric instability of downward propagating flames

This work proposes a new method to estimate the Markstein number by investigating the thermoacoustic parametric instability of laminar premixed flames propagating downwards in an open-closed tube. Methane-air flames were propagated in a combustion tube to capture the flame evolution in transition to parametric instability. By synchronized high-speed imaging filming both lateral and longitudinal views of flame propagation, cellular flame wavenumbers are measured from the clear transition of flat flames to cellular flames visualized in the present approach. The Markstein number is indirectly determined from wavenumber measurements at the onset of parametric instability by employing a laminar flame model under acoustic excitation treating the Markstein number as a free parameter. Acoustic velocity fluctuation amplitudes obtained from pressure fluctuation measurements were determined to further evaluate the validity of wavenumber-derived Markstein numbers. Markstein numbers obtained in the present work are compared with Markstein numbers relative to fresh gases in the literature from indirect and computational methods.